Table 3: Equations to derive the disk/torus properties from observations. Velocities are in units of km s^-1, radii in pc, masses in $M_{\odot }$ , and star formation rates in $M_{\odot }$ yr^-1.
Present collisional torus

$Q^{\rm pr}=(v_{\rm turb}^{\rm pr}/v_{\rm rot})~(M_{\rm dyn}/M_{\rm gas}^{\rm pr})$

$\vartheta^{\rm pr}=1.9 \times 10^{-9} Q^{\rm pr} R/(v_{\rm rot} v_{\rm turb}^{\rm pr} M_{\rm cl})$

$\dot{M}^{\rm pr}=2~(v_{\rm turb}^{\rm pr})^{3}/(G Q^{\rm pr} \vartheta^{\rm pr})$

Massive turbulent gas disk

$Q^{\rm disk}=9674~\dot{M}_*^{-\frac{2}{11}} v_{\rm rot}$

$M_{\rm gas}^{\rm disk}=3.97 \times 10^{5} \dot{M}_*^{\frac{5}{11}} R$

$v_{\rm turb}^{\rm disk}=18.2~\dot{M}_*^{\frac{3}{11}}$

Initial collisional torus

$\dot{M}^{\rm init}=\dot{M} (M_{\rm gas}^{\rm disk}/M_{\rm gas}^{\rm pr})^{2}$

$Q^{\rm init}=Q^{\rm pr} M_{\rm gas}^{\rm pr}/M_{\rm gas}^{\rm disk}$

$\vartheta^{\rm init}=\vartheta^{\rm pr}~M_{\rm gas}^{\rm pr}/M_{\rm gas}^{\rm disk}$

**Table 3:** Equations to derive the disk/torus properties from observations. Velocities are in units of km s^-1, radii in pc, masses in $M_{\odot }$ , and star formation rates in $M_{\odot }$ yr^-1.
Present collisional torus
$Q^{\rm pr}=(v_{\rm turb}^{\rm pr}/v_{\rm rot})~(M_{\rm dyn}/M_{\rm gas}^{\rm pr})$
$\vartheta^{\rm pr}=1.9 \times 10^{-9} Q^{\rm pr} R/(v_{\rm rot} v_{\rm turb}^{\rm pr} M_{\rm cl})$
$\dot{M}^{\rm pr}=2~(v_{\rm turb}^{\rm pr})^{3}/(G Q^{\rm pr} \vartheta^{\rm pr})$
Massive turbulent gas disk
$Q^{\rm disk}=9674~\dot{M}_*^{-\frac{2}{11}} v_{\rm rot}$
$M_{\rm gas}^{\rm disk}=3.97 \times 10^{5} \dot{M}_*^{\frac{5}{11}} R$
$v_{\rm turb}^{\rm disk}=18.2~\dot{M}_*^{\frac{3}{11}}$
Initial collisional torus
$\dot{M}^{\rm init}=\dot{M} (M_{\rm gas}^{\rm disk}/M_{\rm gas}^{\rm pr})^{2}$
$Q^{\rm init}=Q^{\rm pr} M_{\rm gas}^{\rm pr}/M_{\rm gas}^{\rm disk}$
$\vartheta^{\rm init}=\vartheta^{\rm pr}~M_{\rm gas}^{\rm pr}/M_{\rm gas}^{\rm disk}$

Source LaTeX | All tables | In the text